Answer:
Therefore, the vector k-h cannot be written in magnitude and direction form if k-h points directly east.
Explanation:
To write the vector k-h in magnitude and direction form, we first need to find the magnitude and direction of the vector k-h.
Magnitude:
The magnitude of a vector is the length or size of the vector. To find the magnitude of k-h, we subtract the magnitude of h from the magnitude of k.
Given that the magnitude of h is 3 units, we need to find the magnitude of k.
Since k points 45° east of true north and k-h points directly east, we can visualize a right triangle with the vectors k, h, and k-h. The angle between k and k-h is 90°, and the angle between h and k-h is 45°.
To find the magnitude of k, we can use the Pythagorean theorem:
k^2 = h^2 + (k-h)^2
Substituting the given values:
k^2 = 3^2 + (k-h)^2
Simplifying the equation:
k^2 = 9 + (k-h)^2
Since k-h points directly east, the horizontal component of k-h is equal to the magnitude of k.
k^2 = 9 + k^2
Simplifying further:
0 = 9
This equation is not possible, which means there is no magnitude for the vector k-h that satisfies the condition of k-h pointing directly east.